تبارك اسم ربك ذي الجلال والإكرام
Tabāraka ismu rabbika dhī al-jalāli wa al-ikrām
Blessed be the name of your Lord, Lord of majesty and honour: said whenever the name of God is mentioned.
What it means
This sentence is the last verse of Surah al-Rahman: “Blessed is the name of your Lord, Possessor of majesty and honour” (55:78). The verb tabāraka means to be blessed and exalted, rich in good. The phrase dhū al-jalāl wa al-ikrām, Possessor of majesty and honour, is a title of God. Muslims say these words, or part of them, when the name of God is mentioned, to show reverence. It is one of several expressions, among them subḥānahu wa taʿālā and jalla jalāluhu, with which the believer marks the divine name. The Quran also uses the same title earlier in the surah (55:27), where it says that the Face of the Lord will remain.
Often misunderstood as
The phrase is not a name of God itself, although people sometimes take it that way; it is a verse of the Quran used as a sign of respect.
What the sources say
A report says that after the final greeting of the prayer the Prophet Muhammad (peace be upon him) would say, “O God, You are Peace and from You comes peace; blessed are You, O Possessor of majesty and honour” (Sahih Muslim). It joins the same title to the prayer’s close.
Term and Arabic as listed in Ismail al Faruqi, Toward Islamic English (International Institute of Islamic Thought, 1995), p. 58, listed as TABĀRAKA ISMU RABBIKA DHĪ AL JALĀL WAL IKRĀM.. The definition is restated here.